funtimes (version 9.1)

ARest: Estimation of Autoregressive (AR) Parameters

Description

Estimate parameters \(\phi\) of autoregressive time series model $$X_t = \sum_{i=1}^p\phi_iX_{t-i} + e_t,$$ by default using robust difference-based estimator and Bayesian information criterion (BIC) to select the order \(p\). This function is employed for time series filtering in the functions notrend_test, sync_test, and wavk_test.

Usage

ARest(x, ar.order = NULL, ar.method = "HVK", ic = c("BIC", "AIC", "none"))

Value

A vector of estimated AR coefficients. Returns numeric(0) if the final \(p=0\).

Arguments

x

a vector containing a univariate time series. Missing values are not allowed.

ar.order

order of the autoregressive model when ic = "none", or the maximal order for IC-based filtering. Default is round(10*log10(length(x))), where x is the time series.

ar.method

method of estimating autoregression coefficients. Default "HVK" delivers robust difference-based estimates by Hall_VanKeilegom_2003;textualfuntimes. Alternatively, options of ar function can be used, such as "burg", "ols", "mle", and "yw".

ic

information criterion used to select the order of autoregressive filter (AIC of BIC), considering models of orders \(p=\) 0,1,...,ar.order. If ic = "none", the AR(\(p\)) model with \(p=\) ar.order is used, without order selection.

Author

Vyacheslav Lyubchich

Details

The formula for information criteria used consistently for all methods: $$IC=n\ln(\hat{\sigma}^2) + (p + 1)k,$$ where \(n\) = length(x), \(p\) is the autoregressive order (\(p + 1\) is the number of model parameters), and \(k\) is the penalty (\(k = \ln(n)\) in BIC, and \(k = 2\) in AIC).

References

See Also

ar, HVK, notrend_test, sync_test, wavk_test

Examples

# Simulate a time series Y:
Y <- arima.sim(n = 200, list(order = c(2, 0, 0), ar = c(-0.7, -0.1)))
plot.ts(Y)

# Estimate the coefficients:
ARest(Y) # HVK, by default
ARest(Y, ar.method = "yw") # Yule--Walker
ARest(Y, ar.method = "burg") # Burg